Question: Solve for $p$, $ -\dfrac{10}{3p - 5} = \dfrac{5p + 1}{9p - 15} - \dfrac{7}{3p - 5} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $3p - 5$ $9p - 15$ and $3p - 5$ The common denominator is $9p - 15$ To get $9p - 15$ in the denominator of the first term, multiply it by $\frac{3}{3}$ $ -\dfrac{10}{3p - 5} \times \dfrac{3}{3} = -\dfrac{30}{9p - 15} $ The denominator of the second term is already $9p - 15$ , so we don't need to change it. To get $9p - 15$ in the denominator of the third term, multiply it by $\frac{3}{3}$ $ -\dfrac{7}{3p - 5} \times \dfrac{3}{3} = -\dfrac{21}{9p - 15} $ This give us: $ -\dfrac{30}{9p - 15} = \dfrac{5p + 1}{9p - 15} - \dfrac{21}{9p - 15} $ If we multiply both sides of the equation by $9p - 15$ , we get: $ -30 = 5p + 1 - 21$ $ -30 = 5p - 20$ $ -10 = 5p $ $ p = -2$